Identification in Matching Games

I study a many-to-many, two-sided, transferable-utility matching game. Consider data on matches or relationships between agents but not on the choice set of each agent. I investigate what economic parameters can be learned from data on equilibrium matches and agent characteristics. Features of a production function, which gives the surplus from a match, are nonparametrically identified. In particular, the ratios of complementarities from multiple pairs of inputs are identified. Also, the ordering of production levels is identified.